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DPQ (version 0.5-9)

Density, Probability, Quantile ('DPQ') Computations

Description

Computations for approximations and alternatives for the 'DPQ' (Density (pdf), Probability (cdf) and Quantile) functions for probability distributions in R. Primary focus is on (central and non-central) beta, gamma and related distributions such as the chi-squared, F, and t. -- For several distribution functions, provide functions implementing formulas from Johnson, Kotz, and Kemp (1992) and Johnson, Kotz, and Balakrishnan (1995) for discrete or continuous distributions respectively. This is for the use of researchers in these numerical approximation implementations, notably for my own use in order to improve standard R pbeta(), qgamma(), ..., etc: {'"dpq"'-functions}.

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Version

Install

install.packages('DPQ')

Monthly Downloads

583

Version

0.5-9

License

GPL (>= 2)

Homepage

https://specfun.r-forge.r-project.org/

Maintainer

Martin Maechler

Last Published

August 23rd, 2024

Functions in DPQ (0.5-9)

Base-2 Representation and Multiplication of Numbers

dhyperBinMolenaar

HyperGeometric (Point) Probabilities via Molenaar's Binomial Approximation

Psi Gamma Functions Workhorse from R's API

Format Numbers in [0,1] with "Precise" Result

Asymptotic Noncentral t Distribution Density by Viechtbauer

Gamma Density Function Alternatives

Accurate exp(x) - 1 - x (for smallish |x|)

Non-central t-Distribution Density - Algorithms and Approximations

Pure R Versions of R's C (Mathlib) dnbinom() Negative Binomial Probabilities

Distribution Utilities "dpq"

Compute 1/Gamma(x+1) - 1 Accurately

R versions of Simple Formulas for Logarithmic Binomial Coefficients

Accurate log(1+x) - x Computation

Compute log( Gamma(x+1) ) Accurately in [-0.2, 1.25]

Compute \(\mathrm{log}\)(1 - \(\mathrm{exp}\)(-a)) and \(\log(1 + \exp(x))\) Numerically Optimally

Gamma Function Versions

Transform Hypergeometric Distribution Parameters to Binomial Probability

Asymptotic Log Gamma Function

Accurate log(gamma(a+1))

(Log) Beta and Ratio of Gammas Approximations

Numerically Stable p1l1(t) = (t+1)*log(1+t) - t

Simple R level Newton Algorithm, Mostly for Didactical Reasons

Continued Fraction Approximation of Log-Related Power Series

Numerical Utilities - Functions, Constants

Compute Logarithm of a Sum with Signed Large Summands

Compute Hypergeometric Probabilities via Binomial Approximations

Pure R Implementation of Old pbeta()

Properly Compute the Logarithm of a Sum (of Exponentials)

Logspace Arithmetix -- Addition and Subtraction

phyperApprAS152

Normal Approximation to cumulative Hyperbolic Distribution -- AS 152

HyperGeometric Distribution via Approximate Binomial Distribution

Peizer's Normal Approximation to the Cumulative Hyperbolic

Pearson's incomplete Beta Approximation to the Hyperbolic Distribution

Plot 2 Noncentral Distribution Curves for Visual Comparison

The Four (4) Symmetric 'phyper()' Calls

Pure R version of R's C level phyper()

Noncentral Beta Probabilities

R-only version of R's original phyper() algorithm

phyperBinMolenaar

HyperGeometric Distribution via Molenaar's Binomial Approximation

Molenaar's Normal Approximations to the Hypergeometric Distribution

Asymptotic Approxmation of (Extreme Tail) 'pnorm()'

Bounds for 1-Phi(.) -- Mill's Ratio related Bounds for pnorm()

Direct Computation of 'ppois()' Poisson Distribution Probabilities

(Approximate) Probabilities of Non-Central Chi-squared Distribution

pt_Witkovsky_Tab1

Viktor Witosky's Table_1 pt() Examples

Accurate \((1+x)^y\), notably for small \(|x|\)

(Probabilities of Non-Central Chi-squared Distribution for Special Cases

pnchisqWienergerm

Wienergerm Approximations to (Non-Central) Chi-squared Probabilities

Non-central t Probability Distribution - Algorithms and Approximations

X to Power of Y -- R C API R_pow()

Approximations to 'qnorm()', i.e., \(z_\alpha\)

Pure R version of R's qnorm() with Diagnostics and Tuning Parameters

Compute (Approximate) Quantiles of the Beta Distribution

Compute Approximate Quantiles of the Chi-Squared Distribution

Asymptotic Approximation to Outer Tail of qnorm()

Pure R Implementation of R's qnbinom() with Tuning Parameters

Compute Approximate Quantiles of Noncentral Chi-Squared Distribution

Pure R Implementation of R's qt() / qnt()

Pure R Implementation of R's qbinom() with Tuning Parameters

Compute (Approximate) Quantiles of the Gamma Distribution

Compute Relative Size of i-th term of Poisson Distribution Series

'uniroot()'-based Computing of t-Distribution Quantiles

Pure R Implementation of R's C-level t-Distribution Quantiles qt()

TOMS 708 Approximation REXP(x) of expm1(x) = exp(x) - 1

Stirling's Error Function - Auxiliary for Gamma, Beta, etc

Pure R Implementation of R's qpois() with Tuning Parameters

Compute Approximate Quantiles of the (Non-Central) t-Distribution

Approximations of the (Noncentral) Chi-Squared Density

Bernoulli Numbers

pbeta() 'bpser' series computation

R's C Mathlib (Rmath) dbinom_raw() Binomial Probability pure R Function

Chebyshev Polynomial Evaluation

Binomial Deviance -- Auxiliary Functions for dgamma() Etc

tools:::Rd_package_title("DPQ")

Compute \(E[\chi_\nu] / \sqrt{\nu}\) useful for t- and chi-Distributions

Normalized Incomplete Beta Function "Like" pbeta()

Compute log(gamma(b)/gamma(a+b)) when b >= 8